Dynamic Crossover in Liquids Near a Liquid-Liquid Critical Point and Application to Critical Materials Separation

Multicomponent liquids can exhibit demixing, where they separate into two liquid phases at temperatures below a critical TC. Fluctuations in composition diverge as TC is approached, producing nanoscale structure in the liquid that affects its properties. We have recently observed the dynamics of these fluctuations near TC using XPCS, where the scattering is strongest and the relaxation times are relatively long. However, the ability to observe faster dynamics further away from TC will allow much broader studies of the physics of fluids, such as deviations from mean-field behavior, and the dynamics at the Widom line. The high coherent flux at ESRF coupled with the fast TEMPUS detector will allow XPCS studies of fluctuations in liquids at much shorter and faster length- and time- scales than were previously accessible. We focus on systems relevant to applications in liquid-liquid extraction of rare earth elements, which are central to several energy and and resource technologies.